LIFTPACK is a software package written in C for fast calculation of 2D
biorthogonal wavelet transforms using the lifting scheme.

The lifting scheme is a new approach for the construction of
"biorthogonal wavelets" entirely in the spatial domain, i.e.,
independent of the Fourier Transform. Constructing wavelets using
lifting consists of three simple phases: the first step or Lazy
wavelet "splits" the data into two subsets, even and odd, the second
step calculates the wavelet coefficients (high pass) as the failure to
"predict" the odd set based on the even, and finally the third step
"updates" the even set using the wavelet coefficients to compute the
scaling function coefficients (low pass). The predict phase ensures
polynomial cancelation in the high pass (vanishing moments of the dual
wavelet) and the update phase ensures preservation of moments in the
low pass (vanishing moments of the primal wavelet). By varying the
order, an entire family of transforms can be built.

The lifting scheme ensures fast calculation of the forward and inverse
wavelet transforms that only involve FIR filters. The transform works
for images of arbitrary size with correct treatment of the
boundaries. Also, all computations can be done in-place.

LIFTPACK implements Haar wavelets and biorthogonal wavelets of even
number of vanishing moments. It also implements biorthogonal wavelet
packets and spatial mustiscale filtering operations for image
processing. Both 1-D and 2-D signals are accepted. All UNIX
platforms are supported. After some modifications, the software runs
under DOS, Windows 3.1/95/NT, and MAC platforms. Running times depend
on the testing platform, but, under UNIX boxes, they are typically
faster than traditional fast wavelet implementations. However, it is
important to take into account that LIFTPACK is a general purpose
library. For a given wavelet, faster implementations can be obtained
by hardwiring the coefficients.